Let AB=a, AC=b and area right triangle ABC=sBy Poncelet we have: a+b=c+2r(ra-r)+(ra-r)=a+b-2rSimplifyingra+r=a+bNow we know that (ab)/2=(a-r)(b-r)s=(a-r)(b-r)Rewriting this expressionr^2=r(a+b)-s................(1)ra+r=a+b can be rewrite this way: rar+r^2=r(a+b)rar+r^2=r(a+b)...............(2)Now rar+r(a+b)-s=r(a+b)s=rarQ.E.D.By Tony Garcia